1.(12) Suppose that two clothing manufacturers, Lands' End and L.L. Bean, are deciding what price to charge for very similar field coats. The cost of producing these coats is $100. The coats are very close substitutes, so customers flock to the seller that offers the lowest price. If both firms offer identical prices, each receives half the customers.For simplicity, assume that the two firms have the choice of pricing at prices of $103, $102, or $101. The profit each firm would earn at various prices (Lands' Ends Profit, LL Bean's Profit) is shown in the payoff matrix below.

LL Bean

$103 $102 $101

$103 ($150, $150) ($0, $220) ($0, $120)

Lands' End $102 ($220, $0) ($110, $110) ($0, $120)

$101 ($120, $0). ($120, $0). ($60, $60)

1. What is the Nash equilibrium and expected profits to LL Bean and Lands' End of this game?

1. Suppose Lands' End and L.L. Bean decide to collude and jointly determine prices?Is this collusion likely to work.Briefly explain why or why not.(Note:don't worry about the legality of collusion in your answer).

c.Suppose this is a mixed strategy game in which LL Bean has a 25% percent chance of choosing a price of $101, a 25% chance of choosing price of $102, and a 50% chance of choosing $103, while Lands End has a 1/3 chance of choosing each strategy.What's the expected payoff to LL Bean?

d.Suppose that in hopes of raising prices, L.L. Bean announces the price for its coat early in the summer (before Lands' End announces their prices).Represent this using a sequential game tree diagram.Will this strategic move be successful for LL Bean?Explain.